| 陈晓东,李明楚,马欣.2-连通半无爪图的最长圈[J].数学研究及应用,2014,34(1):33~42 |
| 2-连通半无爪图的最长圈 |
| Longest Cycles in 2-Connected Quasi-Claw-Free Graphs |
| 投稿时间：2012-06-04 修订日期：2013-07-07 |
| DOI：10.3770/j.issn:2095-2651.2014.01.003 |
| 中文关键词: 半无爪图 无爪图. |
| 英文关键词:quasi-claw-free graph claw-free graph. |
| 基金项目:国家自然科学基金(Grant No.60673046). |
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| 中文摘要: |
| 若一个图$G$满足下述条件：$d(x,y)=2\Rightarrow$存在一点$u\in N(x)\cap N(y),$ 使得$N[u]\subseteq N[x]\cup N[y],$ 则称$G$为半无爪图. 在这篇文章中,我们证明了若$G$为一个$n$阶图且$G\notin\mathcal{F},$ 则图$G$中含有一个长度至少为min$\{3\delta+2,n\}$的圈, 其中$\mathcal{F}$是一族图. |
| 英文摘要: |
| A graph $G$ is called quasi-claw-free if it satisfies the property: $d(x,y)=2\Rightarrow$ there exists a vertex $u\in N(x)\cap N(y)$ such that $N[u]\subseteq N[x]\cup N[y]$. In this paper, we show that every 2-connected quasi-claw-free graph of order $n$ with $G\notin \mathcal{F}$ contains a cycle of length at least min$\{3\delta+2,n\}$, where $\mathcal{F}$ is a family of graphs. |
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